What is the derivative of (2^x/(cos(x))) ?

The derivative of (2^x/(cos(x))) is 2^xln(2)sec(x)+sec(x)tan(x)*2^x

What is the first derivative of (2^x/(cos(x))) ?

The first derivative of (2^x/(cos(x))) is 2^xln(2)sec(x)+sec(x)tan(x)*2^x

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\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

2^{x} ln (2) sec (x) + sec (x) tan (x) \cdot 2^{x}

Solution steps

\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

Simplify

\frac{2 ^{x}}{cos ( x )} : 2^{x} sec (x)

= \frac{d}{d x} (2^{x} sec (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2^{x}, g = sec (x)

= \frac{d}{d x} (2^{x}) sec (x) + \frac{d}{d x} (sec (x)) 2^{x}

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 2^{x} ln (2) sec (x) + sec (x) tan (x) \cdot 2^{x}

y^{^{''}} + 2 y^{^{'}} + y = 64 e^{(7 t)}

\frac{d}{d x} ((x - 3)^{- 2})

\frac{\partial}{\partial x} (\frac{2 x}{2 y})

3^{x^{2}}

y^{^{'}} = \frac{3 sec ( y )}{( x - 4 ) ^{2}}

What is the derivative of (2^x/(cos(x))) ?
The derivative of (2^x/(cos(x))) is 2^xln(2)sec(x)+sec(x)tan(x)*2^x
What is the first derivative of (2^x/(cos(x))) ?
The first derivative of (2^x/(cos(x))) is 2^xln(2)sec(x)+sec(x)tan(x)*2^x